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Astron. Astrophys. 351, 413-432 (1999)

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1. Introduction

A number of Giant luminous arcs (GLAs) have now been detected in many distant clusters of galaxies (e.g. Soucail et al. 1987; Lynds & Petrosian 1986; Fort & Mellier 1994 for a review). Their spectroscopic confirmations as lensed normal distant galaxies (e.g. Soucail et al. 1988) lead to exciting new cosmological developments in this decade.

Probing the mass distribution of distant clusters is one of avenues of these developments (e.g. Narayan & Bartelmann 1995; Hattori et al. 1999; Umetsu et al. 1999). Early analyses pointed out discrepancy of a factor 2-3 between cluster masses derived from strong lensing and standard X-ray analysis of the ICM (e.g. Loeb & Mao 1994; Miralda-Escudé & Babul 1995). Several possible solutions are proposed: (i) Loeb & Mao 1994 proposed that non-thermal pressure due to equipartition magnetic field and turbulent may play an important role on supporting the ICM. (ii) A multi-phase model of the ICM in the central part of clusters - indicated by the cooling flow model (Allen et al. 1996) - increases by a factor 2-3 the mass deduced from X-ray compared to standard (single-phase) isothermal model (Allen 1998). (iii) Leaving from "inappropriate modeling of the cluster mass distribution due to neglecting the contributions by substructure and member galaxies", which leads overestimation of the cluster mass from strong lensing events (e.g. Kneib et al. 1993; Kneib et al. 1995; Kneib et al. 1996; Hattori et al. 1998). One can expect that the next generation X-ray telescopes (Chandra, XMM, Astro-E) will provide definite answer of the first two possible solutions. The third one seems, however, the closest one to the reality (Hattori et al. 1999).

Instead of these detailed analyses for individual clusters, Statistics of GLAs constrains the average properties of cluster mass distribution. The statistics of GLAs is consist in counting the number of GLAs in a well defined cluster sample and constrains the average properties of cluster mass distribution. Using spherically symmetric mass distribution models, Wu & Hammer (1993) showed that the predicted number of GLAs was critically dependent on the degree of the central mass concentration of clusters. Miralda-Escudé (1993a) examined arc statistics with elliptical lens models and concluded that elliptical mass distribution did not change the above conclusion drastically. Using numerically simulated model for clusters, Bartelmann and his collaborators (Bartelmann & Weiss 1994; Bartelmann et al. 1995, henceforth BSW95) showed that their asymmetric cluster mass distribution (e.g. substructure) increased the expected number of GLAs. In a further study, Bartelmann et al. (1998) examined the dependence of arc statistics on cosmological parameters. They concluded that the open cold dark matter model gave the largest number of giant arcs compared to other cosmology, in particular the Einstein-de Sitter universe and that the open cold dark matter model was likely to be the only model which could match current observations.

The first well-defined GLA survey was conducted by Le Fèvre et al. (1994, henceforth LF94). Hattori et al. (1997, henceforth Paper I) proposed a method that predicted the number of GLAs taking into account both detection conditions in the arc survey and the evolution of source galaxies. They applied their method to the LF94 arc survey sample using the Einstein X-ray data to calibrate the mass distribution - assuming the hydrostatic equilibrium and the spherical symmetry. The conclusion of Paper I is that the expected number of GLAs deduced from the X-ray analysis was inconsistent with the observed one. Hamana & Futamase (1997, henceforth HF97) examined the GLA statistics taking into account the evolution of the luminosity function found by the Canada France Redshift Survey (Lilly et al. 1995). They showed that the observed evolution in the galaxy luminosity function increased the expected GLA number by a factor of 2-3 at most. Although the [FORMULA] relation adopted by them and by Wu & Hammer (1993) appeared to be incorrect when compared with recent results (e.g. Mushotzky & Scharf 1997; Markevitch 1998), we can study how sensitive the GLA statistics is on the evolution of the galaxy luminosity function.

This paper is the second in a series on the giant luminous arc statistics with the LF94 arc survey sample. In this paper we re-visit the LF94 sample with higher quality ROSAT HRI data because no precise measurements of the ICM spatial distribution in the LF94 sample clusters were available in Paper I. We assume that the mass distribution in clusters are spherically symmetric. This paper is organized as follows. In Sect. 2, we briefly summarize the cluster sample and describe its data reduction and analysis. X-ray properties of the sample are described in Sect. 3. In Sect. 4, we describe the lensing properties of mass models. We discuss the GLA statistics and its implication in Sect. 5, and summarize our conclusion in Sect. 6. Notes on individual clusters, as well as contour plot and radial profile of each cluster, are given in the appendix. Throughout this paper, we adopt a Hubble constant of [FORMULA], the present density parameter of [FORMULA], and the present cosmological parameter of [FORMULA].

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© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999